Robust diagnosis and fault-tolerant control of uncertain distributed processes with limited measurements

Abstract

This work develops a robust fault detection and isolation (FDI) and fault-tolerant control (FTC) structure for distributed processes modeled by nonlinear parabolic PDEs with control constraints, time-varying uncertain variables and a finite number of output measurements with limited accuracy. To facilitate the controller synthesis and fault diagnosis tasks, a finite-dimensional system that approximates the dominant dynamic modes of the PDE is initially derived and transformed to a form where each dominant mode is excited directly by only one actuator. A robustly stabilizing bounded output feedback controller is then designed for each dominant mode. The controller synthesis procedure facilitates the derivation of (1) an explicit characterization of the fault-free behavior of each mode in terms of a time-varying bound on the dissipation rate of the corresponding Lyapunov function which accounts for the uncertainty and measurement errors, and (2) an explicit characterization of the robust stability region where constraint satisfaction and robustness with respect to uncertainty and measurement errors are guaranteed. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI, the detection and isolation of faults in a given actuator is accomplished by monitoring the evolution of the dominant modes within the corresponding stability region and declaring a fault when the threshold is exceeded. Robustness of the FDI scheme to measurement errors is ensured by confining the FDI region to an appropriate subset of the stability region, and enlarging the FDI thresholds appropriately. It is shown that these safeguards can be tuned by appropriate selection of the sensor configuration. Finally, the implementation of the FTC architecture on the infinite-dimensional system is discussed and the proposed methodology is demonstrated using a diffusion-reaction process example.